Gravitational and Electric Fields Flashcards
What is a force field?
A region which a body experiences a non-contact force
Give an example of a force field
Gravitational field
What causes a force field?
Interactions between objects or particles e.g. between static or moving charges
What can be said about the affect of gravitational fields around objects of large mass?
Only objects with a large mass, such as planets or stars, have gravitational fields that produce a significant effect
What can be said about the affect of gravitational fields around objects of small mass?
Small objects still have a gravitational field that attracts other objects. but the effect is too weak to be noticeable
How do you represent force fields?
With vector lines, showing the direction of the force they would exert on an object placed in that field
Describe the Earth’s gravitational field
It is radial, so all the lines of force meet in the centre of the Earth
The further apart the vector lines on a force field diagram, the…?
Smaller the force an object placed in the field would experience
Is the force experienced by an object in a gravitational field attractive or repulsive?
Always attractive
What is a point mass?
An object that behaves as if all their mass is concentrated at the centre
What is the equation for Newton’s Law of Gravitation?
F = Gm1m2 / r^2
F: Magnitude of force G: Gravitational constant m1: Mass of 1st object m2: Mass of 2nd object r: Distance between the centres of 2 masses
Describe the proportionality for the Law of Gravitation
It is an inverse square law, so F ∝ 1/r^2
For Newton’s 3rd Law, why don’t we notice the equal and opposite force of the Earth accelerating towards us when we’re falling to the ground?
Because the mass of the Earth is so much larger, F=ma, that the acceleration becomes so incredibly small it’s negligible
Describe the magnitude of the force when the distance between the 2 masses is doubled
Because F ∝ 1/r^2, the force will be 1/4 the strength of the original force
Why is the law of gravitation an inverse square law?
Because it’s radial, so the force at any point with a set distance r will be the same
What is the gravitational field strength?
The force per unit mass
What is the equation for gravitational field strength?
g = F/m
g: Gravitational field strength
F: Force experienced by mass
m: Mass
What are the units of gravitational field strength?
Nkg^-1
What is the approximate value of g at the Earths surface?
9.81 Nkg^-1
What is the equation for the magnitude of a radial gravitational field strength?
g = GM/r^2
g: Magnitude of gravitational field strength
G: Gravitational constant
M: Mass of object creating gravitational field
r: Distance from the centre or distance from point mass
Describe the gravitational field of a point mass
It is a radial gravitational field
Describe what happens to g as you get further away from the Earths surface
g is greatest at the Earths surface, then decreases rapidly as r increases and you move further away from the centre
How do you combine gravitational fields?
Because they’re vectors, you can add them up to find the combined effect of more than one object
What is the direction of an objects gravitational field?
Towards the object, because it’s an attractive force
What is the gravitational potential at a point, V?
The gravitational potential energy that a unit mass at that point would have
What are the units of gravitational potential?
J kg^-1
What is the equation for the gravitational potential in a radial field?
V = - (GM/r)
V: Gravitational potential
G: Gravitational constant
M: Mass of object causing field
r: Distance from centre of object
Is the gravitational potential a negative or positive value at the surface of the mass causing the field?
Negative
Why is the gravitational potential a negative value at the surface of the mass causing the field?
The negative energy can be thought as being caused by you having to do work out against the gravitational field to move an object out of it
What happens to the gravitational potential as distance from the centre of the mass increases?
It increases (tends to zero because it’s a negative value)
What is the value of gravitational potential at an infinite distance from the centre of the object?
0
Is gravitational potential energy a positive or negative value?
Negative (using equation g.p.e = mgh gives positive because that’s the gain in potential energy)
What is the equation for gravitational field strength, using gravitational potential and change in distance?
g = - (ΔV / Δr)
g: Gravitational field strength
ΔV: Change in gravitational potential
Δr: Change in distance from centre of object
What is the gradient of a V-r (gravitational potential-distance from centre) graph equal to?
-g = -gravitational field strength
What is the area under a g-r (gravitational field strength-distance from centre) graph equal to?
Change in gravitational potential between 2 radial distances
Describe the proportionality of gravitational potential (V) and distance from centre (r)?
V ∝ 1/r
What is the gravitational difference?
The energy needed to move a unit mass between 2 points in a gravitational field
What is the equation for gravitational potential difference?
ΔW = mΔV
ΔW: Work done
m: Mass
ΔV: Gravitational potential difference
What are equipotentials?
Lines (2D) and surfaces (3D) that join together all of the points with the same gravitational potential
Describe the change of gravitational potential as you travel along an equipotential
The potential doesn’t change
Describe the gravitational potential difference and the work done between 2 points on an equipotential
ΔV = 0 because the potential doesn’t change, so this means the work done is also equal to 0
Give an example of an object which travels along an equipotential surface
A satellite travelling in a circular orbit
What keeps planets and satellites in orbit?
By the (centripetal) force of gravity from the larger mass that they’re orbiting
What is the gravitational force acting on an orbiting object equal to?
The centripetal force
What is the orbital period?
The time taken for a satellite to complete a full orbit
What is the orbital speed?
The speed that a satellite travels at
What is a satellite?
An object of smaller mass which orbits a larger mass
Give 2 examples of satellites and what each one orbits
Moon is a satellite of the Earth
Earth is a satellite of the Sun
Describe the proportionality between the orbital period and the radius of its orbit
T ∝ √(r^3) OR T^2 ∝ r^3
The greater the radius of a satellites orbit, the…..it will travel and the….it will take to complete a full orbit
The greater the radius of a satellites orbit, the SLOWER it will travel and the LONGER it will take to complete a full orbit
Describe the kinetic energy and the potential energy of a satellite in a circular orbit and explain why?
Both are constant, because in a circular orbit the orbit speed and distance above the mass it’s orbiting stays the same
Describe the total energy of a satellite in an elliptical orbit
It remains constant
Describe the kinetic energy and potential energy of a satellite in an elliptical orbit
A satellites orbital speed will increase as the orbital radius decreases, so the kinetic energy increases as the potential energy decreases (and vice versa)
What is the escape velocity?
The minimum speed an unpowered object needs in order to leave the gravitational field of a planet and not fall back to Earth due to gravitational attraction
What is the equation for the escape velocity?
v = √(2GM/r)
v: Esca[e velocity
G: Gravitational constant
M: Mass of planet
r: Distance of object from centre of planet
How do you derive the equation for escape velocity?
Kinetic energy lost = gravitational potential energy gained
0.5mv^2 = GMm / r
How long would a synchronous orbit or Earth take?
Around 24 hours
What is a synchronous orbit?
When an orbiting object has an orbital period equal to the rotational period of the object it’s orbiting
What are geostationary satellites?
An Earth satellite that orbits directly over the equator and is always above the same point on Earth
What is the period of a geostationary satellite?
24 hours
What is the approximate orbital radius of a geostationary satellite?
42000km, making it about 36000km above the Earths surface
Give 2 examples of uses for geostationary satellites?
TV signals
Telephone signals
What are low orbiting satellites?
Satellites that which orbit between 180 and 2000km above Earth
Why are low orbiting satellites used for communications?
Because they’re cheap to launch and don’t have to have a very powerful transmitter
Give an example of a low orbiting satellite
The ISS (International Space Station)
What’s the main difference between electric fields and gravitational fields?
Electric fields can be attractive or repulsive whereas gravitational fields are only attractive
How does an electric field form?
Any charged object has a region where it can attract or repel other charges
What is the equation for Coulomb’s law?
F = 1/(4π ε0) x (Q1Q2)/r^2
F: Force on object
ε0: Permittivity of free space
Q1 and Q2: Charges of 2 objects
r: Distance between Q1 and Q2
What is permittivity?
A measure of how difficult it is to create an electric field in that object
What type of law is Coulomb’s law?
An example of an inverse square law
Why is Coulomb’s law an inverse square law?
F ∝ 1/r^2
What is a point charge?
A charge with negligible volume or a uniform sphere whose charge acts as if it’s concentrated at the centre
Describe the force of the electric field when the 2 charge points get further away
The force decreases
What is the electric field strength defined as?
Force per unit positive charge
What is the equation for electric field strength?
E = F/Q
E: Electric field strength
F: Force on charged object
Q: Charge of object
What are the units of electric field strength?
NC^-1
What type of quantity is electric field strength?
Vector, because it has direction and magnitude
What does electric field line drawings show?
To show the direction of the force that would act on a positive/negative charge
Describe the field of a point charge
It is a radial field
Which ways do electric field lines point for a positive point charge?
Point away from the point charge
Which ways do electric field lines point for a negative point charge?
Point towards the point charge
Which way do field lines point for parallel plates?
Point from the plate with the more positive voltage towards the plate with the smaller positive voltage (or negative voltage)
What is conducting paper used for?
Can be used to map out the field lines of a 2D electric field
How do you use conducting paper to map out the electric field lines?
Set up so positive charge is on one edge and negative charge is on the opposite edge of the paper. Use a voltmeter at different points on the paper to measure the voltages. Points with the same voltage can be joined up to show equipotential lines
How do equipotential lines link to field lines?
They are perpendicular to each other
What is an electrolytic tank?
A tank of water with 2 electrodes which can be used to map out field lines
How do you use an electrolytic tank to map out the field lines?
Set up the electrolytic tank with water containing positive and negative ions dissolved in it. Place 2 oppositely charged electrodes on either side of the tank. Use a voltmeter to find different points in the water that have the same potential difference. Join them up to draw the equipotential lines
What is the equation for the electric field strength of a point charge radial field?
E = 1/(4π ε0) x Q/r^2
E: Electric field strength
ε0: Permittivity of free space
Q: Point charge
r: Distance from point charge
For a charge that isn’t a point charge (e.g. a metal sphere), does the electric field strength follow the same inverse square law inside the object as outside the object?
Outside of the object, E ∝ 1/r^2, but inside the object the field strength is not proportional to 1/r^2
For a graph of electric field strength (E) against distance from point charge (r) for a point charge, what happens to E as r tends to 0?
E tends to infinity
How is a uniform electric field created?
By connecting 2 parallel plates to the opposite poles of a battery
What is the equation for the electric field strength in uniform fields?
E = V/d
E: Electric field strength
V: Potential difference between the plates
d: Distance between plates
What are the 2 units for electric field strength?
NC^-1 or Vm^-1
If the parallel plate on the bottom has a potential of 0V, what is the potential difference between the 2 plates equal to?
The potential of the top plate
How can you use a uniform electric field to see if a particle is charged or not?
The path of a charged particle in an electric field (perpendicular to field lines) will bend. The direction will depend if it’s positive or negatively charged
Why does the path of a positively charged particle entering an electric field at right angles to the field bend?
The force acts on it in the same direction as the field lines, causing the particle to accelerate at right angles to it’s original motion, so it’s path will bend in that direction
Why does the path of a negaitively charged particle entering an electric field at right angles to the field bend?
The force is in the opposite direction to the field lines, causing the particle to accelerate at right angles to it’s original motion, so it’s path will bend in that direction
What is electric potential energy?
The energy stored by a charge due to its position in an electric field
What does the electric potential energy equal?
The work done moving a charge from infinity to the position
What is the absolute electric potential?
The electric potential energy a unit positive charge (+1C) would have at a specific point
What 2 things does the absolute electric potential depend on?
How far it is away from the charge creating the electric field
Size of that charge
What is the equation for the absolute electric potential of a radial field?
V = 1/(4π ε0) x Q/r
V: Absolute electric potential
ε0: Permittivity of free space
Q: Charge creating electric field
r: Distance from the charge
What happens to the magnitude of V (absolute electric potential) as the distance from the charge increases?
Magnitude of V gets smaller
At what point is the magnitude of V (absolute electric potential) largest?
At the surface of the charge creating the electric field
At what point is the magnitude of V (absolute electric potential) equal to 0?
At infinite distance from the charge
Is V (absolute electric potential) a positive or negative value for a positive charge (repulsive force)?
Positive
Is V (absolute electric potential) a positive or negative value for a negative charge (attractive force)?
Negative
For a graph of V (absolute electric potential) against r (distance from charge), how do you find the electric field strength?
Draw a tangent to the graph at a point and work out the gradient
How do you work out the change in potential?
Change in potential = Final potential - Initial potential
What is the electric potential difference?
The potential difference between 2 points in an electric field with a different absolute electric potential
What is the electric potential difference equal to?
The work needed to move a unit charge between the 2 points
For a graph of radial electric field strength against radial distance (E-r graph), how do you find the electric potential difference?
The area under the graph between points r1 and r2
What is the equation for the amount of energy needed in moving a charge?
W = QΔV
W: Work done in moving charge
Q: Charge being moved
V: Electric potential difference
What do the equipotentials look like for a radial electric field of a point charge?
Spheres
What do the equipotentials look like for an electric field between 2 parallel plates?
Flat planes
What is the work done equal to as you travel along an equipotential?
0 because no work is done as all the electric potential/gravitational potential difference is 0
What is the similarity between the definition of gravitational field strength and electric field strength?
Gravitational field strength is force per unit mass. Electric field strength is force per unit charge
How does Newton’s Law of Gravitation and Coulomb’s Law compare?
They’re both inverse square laws
